Indeterminate Probabilities

Abstract

It has been objected against the subjectivistic interpretation of probability that it assumes that a subject’s degree of belief P(E) in any event or proposition E is an exact numerical magnitude which might be evaluated to any desired number of decimal places. This is believed to follow from the fact that if a system of degrees of belief expressed by the function P can interpret the exact quantitative probability calculus, it must be the case for every real number p and every event E under consideration that either P(E) = p or P(E) ≠p. The same argument, however, would appear to show that no empirical magnitude can satisfy laws expressed in the classical logico-mathematical framework, so long as it is granted that indeterminacy, to a greater or lesser extent, is present in all empirical concepts. It would apply, for instance, to the concept of length. More to the point, it would apply to any empirical interpretation of probability whether subjectivistic or not.